Trigonometric Curves

The three main trigonometric graphs are:

  • Sine graph
  • Cosine graph
  • Tan graph

Sine Graph

sinegraph
x0 sin x
00
901
1800
270-1
3600

Characteristics:

  • Period is 3600. It repeats itself every 360 degrees.
  • Maximum value = +1
  • Minimum value = -1

Cosine Graph

cosgraph
x0 cos x
01
900
180-1
2700
3601

Characteristics:

  • Period is 3600. It repeats itself every 360 degrees.
  • Maximum value = +1
  • Minimum value = -1

Tan Graph

tangraph
x0 tan x
00
90
1800
270
3600

Characteristics:

  • Period is 1800. It repeats itself every 180 degrees.
  • Maximum value = +∞
  • Minimum value = -∞

Transformation of a Graph

transformation
x0sin x2 sin x1 + 2 sin x
0001
90123
180001
270-1-2-1
360001

This is stretched by a factor 2 parallel to the y-axis and then moved up by 1 - a translation of 1 in the positive y-axis.

Now, in order to complement what you have just learnt, work out the following questions:

>
  1. Sketch the following graphs:
    • 2 cos x
    • 1 - 3 sin x
    • 2 tan x
    • 2 + 3 sin x
  2. Find the period, maximum value and minimum value of the following functions:
    • 3 cos x
    • 1 - 2sin 2x
    • 3 cos 2x
    • 2 + 3 sin x/2

 

 

 

 

 

Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

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Recommended Reading

 

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